Multivariate Calculus & Ordinary Differential Equations (MATH1052)

Course overview

(MATH1052 can be studied concurrently with MATH1051)

Vector calculus, arclength, line integrals, applications. Calculus of 2 & 3 variables: partial derivatives, conservative fields, Taylor series, maxima & minima, non-linear equations. 1st order & linear 2nd order differential equations (constant coefficients). Applications (dynamical systems etc), numerical methods.

The first part of MATH1052 introduces ordinary differential equations (ODEs), one of the basic tools in mathematical modelling. In science and engineering, ODEs are used to describe, for instance, the motion of particles and satellites, the rate of chemical reactions or the behaviour of electrical circuits. In biology, ODEs are used to describe population dynamics, for example to model epidemics.

The secondﾠpart of MATH1052 extends your knowledge of calculus to functions of more than one variable. This enables you to differentiate multivariate functions and find maxima and minima. These ideas are basic to optimisation found in many applications such as finance, economics and engineering.

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Course requirements

Assumed background

MATH1052ﾠassumes knowledge of MATH1051/1071.ﾠﾠIt is highly recommended that you have studied MATH1051/1071. However, it is possible to take MATH1051ﾠand MATH1052ﾠin the same semester.ﾠIn this case,ﾠyou should have achieved a grade B or higher in Queensland Year 12 Specialist Mathematics (or equivalent) or obtained a credit of better in MATH1050.

Algebra:ﾠFinding roots and factoring polynomials. Expansion and simplification of algebraic expressions. Trigonometric functions and identities. Logarithms and the exponential function. Solving systems of linear equations. Complex numbers.

Calculus of one variable:ﾠLimits, continuity, and derivatives. Finding maxima and minima. The indefinite integral, the definite integral and area.

Advanced Calculus:ﾠTechniques of integration (substitution, parts, trig substitutions, partial fractions). The Taylorﾠseries. (These are taught in MATH1051 before they are needed in MATH1052.)

Vectors:ﾠVectors in 2D and 3D space. Addition of vectors. Angles between vectors; 2 X 2 matrices and inverses.

Matlab:ﾠStudents should have an understanding of the basics in Matlab: command line calculations, writing small programs and functions, loops, vectors and matrices andﾠezplotﾠplotting. (This material will be taught in MATH1051 before it is needed in MATH1052.)

Prerequisites

You'll need to complete the following courses before enrolling in this one:

MATH1050 or a grade of C or higher in Queensland Year 12 Specialist Mathematics (Units 3 & 4) (or equivalent).

Incompatible

You can't enrol in this course if you've already completed the following:

MATH1072, MATH7052 (co-taught)

Course contact

Course staff

Timetable

The timetable for this course is available on the UQ Public Timetable.

Additional timetable information

All classes will be conducted on campus. Consult your personal timetable for times and locations. Students are expected to attend classes unless they have a valid reason for being unable to attend (such as illness).

 IMPORTANT: If you are ill, then do not attend any classes in person.  You can follow lectures on UQ Extend and attend another workshop during the week.

There will be no classes on Ekka Show day and the King's birthday. Alternative arrangements will be made and communicated via Blackboard.

You may follow lectures in any of the following ways:

• face-to-face lectures (preferred!)
• pre-recordings on UQ Extend, 
• lecture recordings (usually available soon after the lecture)
• Zoom livestream

Lectures and workshops will begin in Week 1.

OPTIONAL:

The Support Learning Tutorial (SLT) is optional. This class is highly recommended for: 

• Students who are repeating MATH1052.
• Students who obtained a Grade 4 in MATH1050/1051.
• Students who obtained a grade C  for Queensland Specialist Mathematics (or equivalent).
• Students who are returning to maths studies after a significant period.

Check Blackboard for further information about the SLT. 

Aims and outcomes

This course aims to give students a foundation knowledge of techniques in multivariate and vector calculus and ordinary differential equations.ﾠ Students should then be able to apply analytical and numerical techniques to problems with real world complexity.

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Learning outcomes

After successfully completing this course you should be able to:

Assessment

Assessment summary

A hurdle is an assessment requirement that must be satisfied in order to receive a specific grade for the course. Check the assessment details for more information about hurdle requirements.

Assessment details

Workshop Exercise

• Team or group-based
• In-person

Mode

Written

Category

Participation/ Student contribution, Tutorial/ Problem Set

Weight

15% Each exercise is marked out of 5. The best 9 marks will count for assessment.

Due date

Week 1: 22/07/2024 - 26/07/2024

Week 2: 29/07/2024 - 2/08/2024

Week 3: 5/08/2024 - 9/08/2024

Week 5: 19/08/2024 - 23/08/2024

Week 6: 26/08/2024 - 30/08/2024

Week 7: 2/09/2024 - 6/09/2024

Week 8: 9/09/2024 - 13/09/2024

Week 9: 16/09/2024 - 20/09/2024

Week 10: 30/09/2024 - 20/09/2024

Week 12: 14/10/2024 - 18/10/2024

Week 13: 21/10/2024 - 25/10/2024

You will submit the collaborative exercise at the end of your workshop. The collaborative exercise includes a MATLAB activity.

Task description

Submission guidelines

Submit ONE collaborative exercise per group at the end of the workshop.

Deferral or extension

You cannot defer or apply for an extension for this assessment.

There are NO extensions for the collaborative exercise. If you are unable to attend your regular workshop, please attend another workshop during the week.

Assignment

Mode

Written

Category

Tutorial/ Problem Set

Weight

15% Each assignment is weighted 7.5%.

Due date

Assignment 1: 16/08/2024 5:00 pm

Assignment 2: 11/10/2024 5:00 pm

Task description

Submission guidelines

Submit via Gradescope. Instructions are on the course Blackboard site.

Deferral or extension

You may be able to apply for an extension.

The maximum extension allowed is 7 days. Extensions are given in multiples of 24 hours.

Solutions for assessment item/s will be released 7 days after the assessment is due. Therefore an extension after 7 days will not be possible.

See ADDITIONAL ASSESSMENT INFORMATION for the extension and deferred examination information relating to this assessment item.

Late submission

A penalty of 10% of the maximum possible mark will be deducted per 24 hours from time submission is due for up to 7 days. After 7 days, you will receive a mark of 0.

You are required to submit assessable items on time. If you fail to meet the submission deadline for any assessment item then the listed penalty will be deducted per day for up to 7 calendar days, at which point any submission will not receive any marks unless an extension has been approved. Each 24-hour block is recorded from the time the submission is due.

In-semester exam

• Hurdle
• Identity Verified
• In-person

Mode

Written

Category

Examination

Weight

20%

Due date

In-semester Saturday

31/08/2024 - 14/09/2024

You must hold all of the following three Saturdays free until the exam date is officially announced:

31 August 2024 (week 6)

7 September 2024 (week 7)

14 September 2024 (week 8)

Other conditions

Time limited.

See the conditions definitions

Task description

Hurdle requirements

Exam details

Submission guidelines

N/A

Deferral or extension

You may be able to defer this exam.

See ADDITIONAL ASSESSMENT INFORMATION for the extension and deferred examination information relating to this assessment item.

End of semester Examination

• Hurdle
• Identity Verified
• In-person

Mode

Written

Category

Examination

Weight

50%

Due date

End of Semester Exam Period

2/11/2024 - 16/11/2024

Other conditions

Time limited.

See the conditions definitions

Task description

Hurdle requirements

Exam details

Submission guidelines

N/A

Deferral or extension

You may be able to defer this exam.

See ADDITIONAL ASSESSMENT INFORMATION for the extension and deferred examination information relating to this assessment item.

Course grading

Full criteria for each grade is available in the Assessment Procedure.

Additional course grading information

Note the requirements to achieve a passing grade (4,5,6 or 7). In summary,

(1) If you do not receive a total score for the course of at least 50%, then you will fail MATH1052.

(2) If you do not eitherﾠ

(i) receive at least 40% of the sum of the marks available for the in-semester exam and the final exam, OR

(ii) receive at least 40% of the marks available for the final exam,ﾠ

then you will fail MATH1052.

Supplementary assessment

Supplementary assessment is available for this course.

Should you fail a course with a grade of 3, you may be eligible for supplementary assessment. Refer to my.UQ for information on supplementary assessment and how to apply. 

Supplementary assessment provides an additional opportunity to demonstrate you have achieved all the required learning outcomes for a course.  

If you apply and are granted supplementary assessment, the type of supplementary assessment set will consider which learning outcome(s) have not been met.  

Supplementary assessment in this course will be a 2-hour examination similar in style to the end-of-semester examination. To receive a passing grade of 3S4, you must obtain a mark of 50% or more on the supplementary assessment. 

Additional assessment information

It is your responsibility to check that the marks for the various assessments have been correctly entered.ﾠIf an error has been made in assessing your work, then contact the course coordinator within 21 calendar days following the release of marks for the assessment piece.ﾠ

Artificial Intelligence

The assessment tasks in this course evaluate students’ abilities, skills and knowledge without the aid of Artificial Intelligence (AI). Students are advised that the use of AI technologies to develop responses is strictly prohibited and may constitute misconduct under the Student Code of Conduct.

Applications for Extensions to Assessment Due Dates

Extension requests are submitted online via my.UQ – applying for an extension. Extension requests received in any other way will not be approved. Additional details associated with extension requests, including acceptable and unacceptable reasons, may be found at my.UQ.

Please note:

• Requests for an extension to an assessment due date must be submitted through your my.UQ portal and you must provide documentation of your circumstances, as soon as it becomes evident that an extension is needed. Your application must be submitted on or before the assessment item's due date and time.
• Applications for extension can take time to be processed so you should continue to work on your assessment item while awaiting a decision. We recommend that you submit any completed work by the due date, and this will be marked if your application is not approved. Should your application be approved, then you will be able to resubmit by the agreed revised due date.
• If an extension is approved, you will be notified via your my.UQ portal and the new date and time for submission provided. It is important that you check the revised date as it may differ from the date that you requested.
• If the basis of the application is a medical condition, applications should be accompanied by a medical certificate dated prior to the assignment due date. If you are unable to provide documentation to support your application by the due date and time you must still submit your application on time and attach a written statement (Word document) outlining why you cannot provide the documentation. You must then upload the documentation to the portal within 24 hours.
• If an extension is being sought on the basis of exceptional circumstances, it must be accompanied by supporting documentation (eg. Statutory declaration).
• For extensions based on a SAP you may be granted a maximum of 7 days (if no earlier maximum date applies). See the Extension or Deferral availability section of each assessment for details. Your SAP is all that is required as documentation to support your application. However, additional extension requests for the assessment item will require the submission of additional supporting documentation e.g., a medical certificate. All extension requests must be received by the assessment due date and time.
• Students may be asked to submit evidence of work completed to date. Lack of adequate progress on your assessment item may result in an extension being denied.
• If you have been ill or unable to attend class for more than 14 days, you are advised to carefully consider whether you are capable of successfully completing your courses this semester. You might be eligible to withdraw without academic penalty - seek advice from the Faculty that administers your program.
• There are no provisions for exemption from an assessment item within UQ rules. If you are unable to submit an assessment piece then, under special circumstances, you may be granted an exemption, but may be required to submit alternative assessment to ensure all learning outcomes are met.

Applications to defer an exam

In certain circumstances you can apply to take a deferred examination for in-semester and end-of-semester exams. You'll need to demonstrate through supporting documentation how unavoidable circumstances prevented you from sitting your exam. If you can’t, you can apply for a one-off discretionary deferred exam.

Deferred Exam requests are submitted online via mySi-net. Requests received in any other way will not be approved. Additional details associated with deferred examinations, including acceptable and unacceptable reasons may be found at my.UQ.

Please note:

• Applications can be submitted no later than 5 calendar days after the date of the original exam.
• There are no provisions to defer a deferred exam. You need to be available to sit your deferred examination.
• Your deferred examination request(s) must have a status of "submitted" in mySI-net to be assessed.
• All applications for deferred in-semester examinations are assessed by the relevant school. Applications for deferred end-of-semester examinations are assessed by the Academic Services Division.
• You’ll receive an email to your student email account when the status of your application is updated.
• If you have a medical condition, mental health condition or disability and require alternative arrangements for your deferred exam you’ll need to complete the online alternative exam arrangements through my.UQ. This is in addition to your deferred examinations request. You need to submit this request on the same day as your request for a deferred exam or supplementary assessment. Contact Student Services if you need assistance completing your alternative exam arrangements request.

Learning resources

You'll need the following resources to successfully complete the course. We've indicated below if you need a personal copy of the reading materials or your own item.

Library resources

Find the required and recommended resources for this course on the UQ Library website.

Other course materials

Additional learning resources information

Blackboard:ﾠInformation about MATH1052, including the workbook, assessment material and announcements, are all available on the Blackboard site. Please check this site regularly for updates.

Reference texts:ﾠ There are many calculus texts in theﾠLibrary; look around the call number QA303.

MATLAB:ﾠMATLAB is available online. Access instructions are on the course Blackboard site.

First-Year Learning Centre: Mon and Thu, 11am-2pm; Tue, Wed, Fri, 1-4 pm. Room 67-443, starting in Week 1.

Support Learning Tutorials (SLTs): These will run on a weekly basis. Details will be announced on the Blackboard site. These are optional activities, and involve working through past exam problems.

Learning activities

The learning activities for this course are outlined below. Learn more about the learning outcomes that apply to this course.

Policies and procedures

University policies and procedures apply to all aspects of student life. As a UQ student, you must comply with University-wide and program-specific requirements, including the:

• Student Code of Conduct Policy
• Student Integrity and Misconduct Policy and Procedure
• Assessment Procedure
• Examinations Procedure
• Reasonable Adjustments - Students Policy and Procedure

Learn more about UQ policies on my.UQ and the Policy and Procedure Library.